Diffraction By An Aperture Ii

Cover Diffraction By An Aperture Ii
Diffraction By An Aperture Ii
Joseph Bishop Keller
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Then the asymptotic value of each integral for k large comes from - 16 - the neighborhoods of the three types of critical points. Once these points are found, it will suffice to know the behavior of the integrands near them in oixier to evaluate the integrals asjinptotically. Therefore it will not be necessary to construct a!q)licltly the complete integrands, which join the interior and edge values together sraoothJ. Y. In the interior of the aperture the integrands of Ug, and Ugp are the same ...as those of u. And u^ respectively. Therefore u_, and u^jp have the sane interior stationary points as u. And Up and also receive the same contribution from each point. If we designate the sum of these contributions by u^, and u^^ then we have Ug, " ^ = ^cecm* ®"^ ^2 " ^ " ^seom* ^^^ ^°*^ \ ^^'^ ^ equal ^geom* II II Let us now locate the edge stationary points and evaluate Ug, and Uggj the contributions to Up, and yx^^ from these points. To do this we must consider the integrands near the edge.

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